On a class of strongly stabilizable systems of neutral type

We consider the strong stabilizability problem for a delayed system of neutral type. For simplicity the case of one delay in state is studied. We separate a class of such systems and give a constructive solution of the problem in this case, without the derivative of the localized delayed state. Our results are based on an abstract theorem on the strong stabilizability of contractive systems in Hilbert space. An illustrating example is also given.     

On the period function in a class of generalized Lotka-Volterra systems

In this note, motivated by the recent results of Wang et al. [Wang et al., Local bifurcations of critical periods in a generalized 2D LV system, Appl. Math. Comput. 214 (2009) 17-25], we study the behaviour of the period function of the center at the point (1,1) of the planar differential system

     

On a new class of elliptic systems with nonlinearities of arbitrary growth

We guarantee the existence of infinitely many different pairs of solutions to the system

     

On a new class of analytic function derived by a fractional differential operator

Making use of the fractional differential operator, we impose and study a new class of analytic functions in the unit disk (type fractional differential equation). The main object of this paper is to investigate inclusion relations, coefficient bound for this class. Moreover, we discuss some geometric properties of the fractional differential operator.     

On a type of matrix splitting preconditioners for a class of block two-by-two linear systems

Recently, Bai et al. (2013) proposed an effective and efficient matrix splitting iterative method, called preconditioned modified Hermitian/skew-Hermitian splitting (PMHSS) iteration method, for two-by-two block linear systems of equations. The eigenvalue distribution of the iterative matrix suggests that the splitting matrix could be advantageously used as a preconditioner. In this study, the CGNR method is utilized for solving the PMHSS preconditioned linear systems, and the performance of the method is considered by estimating the condition number of the normal equations. Furthermore, the proposed method is compared with other PMHSS preconditioned Krylov subspace methods by solving linear systems arising in complex partial differential equations and a distributed control problem. The numerical results demonstrate the difference in the performance of the methods under consideration.     

ON GLOBAL SOLUTION FOR A CLASS OF SYSTEMS OF MULTI－DIMENSIONAL GENERALIZED ZAKHAROV TYPE EQUATION

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On a class of semilinear elliptic systems

This paper deals with the existence of positive solutions to a Dirichlet problem for the superlinear elliptic system

Δu=−λf(v),Δv=−λg(u)     

On a class of strongly hyperbolic systems

In this paper we prove a well-posedness result for the Cauchy problem. We study a class of first order hyperbolic differential [2] operators of rank zero on an involutive submanifold ofT ^* R ⁿ⁺¹-{0} and prove that under suitable assumptions on the symmetrizability of the lifting of the principal symbol to a natural blow up of the “singular part” of the characteristic set, the operator is strongly hyperbolic.     

On a class of weak Tchebycheff systems

In this paper we study the approximation power, the existence of a normalized B-basis and the structure of a degree-raising process for spaces of the formrequiring suitable assumptions on the functions u and v. The results about degree raising are detailed for special spaces of this form which have been recently introduced in the area of CAGD.     

On a class of Kirchhoff type problems

In this paper we consider the following Kirchhoff type problem: $$(\mathcal{K}) \quad \left(1 + \lambda \int\limits_{\mathbb{R}^3}\big(|\nabla u|^2 + V(y)u^2dy\big)\right)[-\Delta u + V(x)u] = |u|^{p-2}u, \quad {\rm in} \, \mathbb{R}^3,$$ where ${p\in (2, 6)}$ , λ > 0 is a parameter, and V(x) is a given potential. Some existence and nonexistence results are obtained by using variational methods. Also, the “energy doubling” property of nodal solutions of ${(\mathcal{K})}$ is discussed in this paper.     

On a class of slowly changing function

The online version of the original article can be found at     

On a new class of elementary matrices

Summary A new class of elementary matrices, a block-generalisation of plane rotations, is presented and the application in constructing quadratically convergent block diagonalisation algorithms of Jacobi type is discussed.     

On a new class of Finsler metrics

In this paper, the geometric meaning of (α,β)-norms is made clear. On this basis, a new class of Finsler metrics called general (α,β)-metrics are introduced, which are defined by a Riemannian metric and a 1-form. These metrics not only generalize (α,β)-metrics naturally, but also include some metrics structured by R. Bryant. The spray coefficients formula of some kinds of general (α,β)-metrics is given and the projective flatness is also discussed.     

On a new class of hyperbolic functions

This article presents the results of some new research on a new class of hyperbolic functions that unite the characteristics of the classical hyperbolic functions and the recurring Fibonacci and Lucas series. The hyperbolic Fibonacci and Lucas functions, which are the being extension of Binet's formulas for the Fibonacci and Lucas numbers in continuous domain, transform the Fibonacci numbers theory into “continuous” theory because every identity for the hyperbolic Fibonacci and Lucas functions has its discrete analogy in the framework of the Fibonacci and Lucas numbers. Taking into consideration a great role played by the hyperbolic functions in geometry and physics, (“Lobatchevski's hyperbolic geometry”, “Four-dimensional Minkowski's world”, etc.), it is possible to expect that the new theory of the hyperbolic functions will bring to new results and interpretations on mathematics, biology, physics, and cosmology. In particular, the result is vital for understanding the relation between transfinitness i.e. fractal geometry and the hyperbolic symmetrical character of the disintegration of the neural vacuum, as pointed out by El Naschie [Chaos Solitons & Fractals 17 (2003) 631].     

On a new class of probability distributions

Multicomponent systems are widely used in computer science. The reliability of these systems plays a very important role in efficient working. These systems are not always supposed to follow the standard probability distributions and so pseudo-distributions can be thought of as suitable alternatives. In this work we have defined a new bivariate pseudo-Weibull distribution. Some standard properties of the distribution have been studied. The distributions of the order statistics and concomitants have also been obtained.     

On a class of new integral inequalities

This paper is concerned with a class of new integral inequalities involving real-valued functions and their derivatives satisfying certain boundary conditions. Our analysis is more elementary and depends on the general theory used in the development of integral inequalities involving functions and their derivatives.     

On a new class of infinite groups

The present paper is devoted to the study of properties of a new class of -groups. The class of layer-finite groups is characterized with an accuracy to within this class.Published in Ukrainskii Matematicheskii Zhurnal, Vol. 47, No.6, pp. 760–769, June, 1995.This work was partially supported by the Russian Foundation for Fundamental Research (Grant 93-01-16003).